Schrödinger Equation and Quantum Shock Waves when Describing Collisions of Atomic Nuclei

Equations of quantum hydrodynamics were obtained from the Schrödinger equation considering dissipation, which in the semiclassical limit are reduced to the conventional equations of hydrodynamics of an ideal fluid. An analytical solution to the hydrodynamic equations was found in the quantum shock wave approximation in one- and two-dimensional cases. The dissipative function can be found using a nonequilibrium approach. A comparison was made with experimental data to describe the emission of protons in collisions of medium-sized atomic nuclei of intermediate energies.